C Géronimi et al 2001 J. Phys. A: Math. Gen. 34 10109 doi:10.1088/0305-4470/34/47/315
C Géronimi1, M R Feix1 and P G L Leach2
Show affiliationsThe conventional approach to double reduction of the order of an ordinary differential equation using Lie symmetries is via the normal subgroups of point symmetries. We show that, provided that one is prepared to use nonlocal symmetries, initial reduction by the nonnormal subgroup does not prevent the double reduction. We further illustrate our results with the general third-order equations invariant under the nonsolvable algebras, sl(2, R) (of which the Chazy equation is a noted example) and so(3).
22E40 Discrete subgroups of Lie groups (See also 20Hxx, 32Nxx)
Issue 47 (30 November 2001)
Received 7 September 2001
Published 16 November 2001
C Géronimi et al 2001 J. Phys. A: Math. Gen. 34 10109
Y Ozeki and H Nishimori 1993 J. Phys. A: Math. Gen. 26 3399
O Céspedes et al 2004 J. Phys.: Condens. Matter 16 L155
R L Becker and A D MacKellar 1984 J. Phys. B: At. Mol. Phys. 17 3923
Julien Oster et al 2009 Physiol. Meas. 30 1381
Heinz-Peter Breuer 2006 J. Phys. A: Math. Gen. 39 11847
H Saint-Guirons and P Xans 1981 J. Phys. E: Sci. Instrum. 14 1332
A S Kheifets 2007 J. Phys. B: At. Mol. Opt. Phys. 40 F313
A D Harken and B W Robertson 2006 J. Phys. D: Appl. Phys. 39 4961
J Hecker Denschlag et al 2002 J. Phys. B: At. Mol. Opt. Phys. 35 3095